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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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CONSTRUCTIONS OF QUANTUM GROUPS WITH THE RAPID DECAY PROPERTY


Prelegent: HUA WANG

2023-01-18 17:15

Starting with Haagerup's seminal work, the rapid decay (RD) property was systematically studied by Jolissaint for discrete groups, and later by Vergnioux, in the setting of discrete quantum groups. Through the work of many hands, the RD property is nowadays an interesting approximation property that has connections to many other fields, such as K-theory, L^2-cohomology, etc. After a motivating introduction, I will quickly review my joint work with Fima on the permanence of the RD property for a large class of bicrossed products, as well as how the natural question of constructing explicit examples leads to an interesting calculation of the fusion rules for certain semi-direct products. Combining these results, I will finish by explaining how to produce some  discrete quantum groups with the RD property but without the polynomial growth.